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Analytic Rasterization of Curves with Polynomial Filters
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BibTeX
@MISC{Manson_analyticrasterization,
author = {Josiah Manson and Scott Schaefer},
title = {Analytic Rasterization of Curves with Polynomial Filters},
year = {}
}
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Abstract
Figure 1: Vector graphic art of butterflies represented by cubic curves, scaled by the golden ratio. The images were analytically rasterized using our method with a radial filter of radius three. We present a method of analytically rasterizing shapes that have curved boundaries and linear color gradients using piecewise polynomial prefilters. By transforming the convolution of filters with the image from an integral over area into a boundary integral, we find closed-form expressions for rasterizing shapes. We show that a polynomial expression can be used to rasterize any combination of polynomial curves and filters. Our rasterizer also handles rational quadratic boundaries, which allows us to evaluate circles and ellipses. We apply our technique to rasterizing vector graphics and show that our derivation gives an efficient implementation as a scanline rasterizer.
Keyphrases
analytic rasterization polynomial filter efficient implementation radial filter closed-form expression polynomial curve vector graphic art linear color gradient cubic curve rational quadratic boundary golden ratio piecewise polynomial prefilters vector graphic polynomial expression scanline rasterizer
